Chesapeake Energy's troubles are far from over, but the company is doing what it can to regain favor with investors. The natural gas giant announced Monday that it is replacing four members of its board of directors, bowing to pressure from two of its largest shareholders, including Carl Icahn.

In fact, Icahn, who owns a 7.56% stake in Chesapeake, may fill one of the open seats at the table himself, the company said. At the very least, Icahn will handpick who fills one of the spots. Southeastern Asset Management, which owns 13.6% of the company, will nominate independent directors for the three remaining open positions. The four current board members, who weren't named, will resign after the new slate is appointed.

Shares of Chesapeake (CHK) rose as much as 3.6% on the news, before pulling back slightly to be up about 2.6%.

The shake-up follows intense shareholder pressure following revelations in April that Chesapeake CEO Aubrey McClendon took out more than $1 billion in loans backed by personal stakes in the firm's wells through an incentive program, raising concerns about a conflict of interest. The board quickly responded by ending the program and announcing that while McClendon will remain CEO of the company and a member of the board, he will no longer serve as chairman.

Despite progress on the corporate governance front, Chesapeake is still struggling financially. The company has been hurt by weak natural gas prices its balance sheet is weighed down by $12.6 billion in long-term debt. The company is trying to sell as much as $14 billion in assets this year to pay down that debt, but said last month that it may have to postpone some previously planned sales of assets, such as oil and gas wells, because they are used to secure its revolving credit line.

Chesapeake shareholders will gather at the company's headquarters in Oklahoma City this Friday for its annual shareholder meeting.